FBX export missing cloth modified mesh
I think the answer is you dont use blender for unreal cloth. I think you make the cape in blender same as any other mesh, then import it into unreal and do the cloth there. Unreal used to use something called apex cloth (which it still can), but now also has its own cloth authoring tools.

Here is a link to a video showing unreals clothing system, if you skip to 5:00 exactly it will show you how to author cloth with the new system in ue4.

https://www.youtube.com/watch?v=4ZN3WHh3M9M